Dose estimates and their uncertainties for use in epidemiological studies of radiation-exposed populations in the Russian Southern Urals

Many residents of the Russian Southern Urals were exposed to radioactive environmental pollution created by the operations of the Mayak Production Association in the mid- 20th century. There were two major releases: the discharge of about 1x1017 Bq of liquid waste into the Techa River between 1949 and 1959; and the atmospheric release of 7.4 * 1016 Bq as a result an explosion in the radioactive waste-storage facility in 1957. The releases into the Techa River resulted in the exposure of more than 30,000 people who lived in riverside villages between 1950 and 1961. The 1957 accident contaminated a larger area with the highest exposure levels in an area that is called the East Urals Radioactive Trace (EURT). Current epidemiologic studies of the exposed populations are based on dose estimates obtained using a Monte-Carlo dosimetry system (TRDS-2016MC) that provides multiple realizations of the annual doses for each cohort member. These dose realizations provide a central estimate of the individual dose and information on the uncertainty of these dose estimates. In addition, the correlation of individual annual doses over realizations provides important information on shared uncertainties that can be used to assess the impact of shared dose uncertainties on risk estimate uncertainty.This paper considers dose uncertainties in the TRDS-2016MC. Individual doses from external and internal radiation sources were reconstructed for 48,036 people based on environmental contamination patterns, residential histories, individual 90Sr body-burden measurements and dietary intakes. Dietary intake of 90Sr resulted in doses accumulated in active bone marrow (or simply, marrow) that were an order of magnitude greater than those in soft tissues. About 84% of the marrow dose and 50% of the stomach dose was associated with internal exposures. The lognormal distribution is well-fitted to the individual dose realizations, which, therefore, could be expressed and easily operated in terms of geometric mean (GM) and geometric standard deviation (GSD). Cohort average GM for marrow and stomach cumulative doses are 0.21 and 0.03 Gy, respectively. Cohort average dose uncertainties in terms of GSD are as follows: for marrow it is 2.93 (90%CI: 2.02–4.34); for stomach and the other non-calcified tissues it is 2.32 (90% CI: 1.78–2.9).

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23
Many residents of the Southern Urals were exposed to radioactive environmental pollution 24 created by the operations of the Mayak Production Association in the mid-20 th century. There 25 were two major releases: the discharge of about 1x10 17 Bq of liquid waste into the Techa River 26 between 1949 and 1959; and the atmospheric release of 7.4 * 10 16 Bq as a result an explosion in 27 the radioactive waste-storage facility in 1957. The releases into the Techa River resulted in the 28 exposure of more than 30,000 people who lived in riverside villages between 1950 and 1961. The 29 1957 accident contaminated a larger area with the highest exposure levels in an area that is called 30 the East Urals Radioactive Trace (EURT). Current epidemiologic studies of the exposed 31 populations are based on dose estimates obtained using a Monte-Carlo dosimetry system (TRDS-32 2016MC) that provides multiple realizations of the annual doses for each cohort member. These 33 dose realizations provide a central estimate of the individual dose and information on the 34 uncertainty of these dose estimates. In addition, the correlation of individual annual doses over 35 realizations provides important information on shared uncertainties that can be used to assess the 36 impact of shared dose uncertainties on risk estimate uncertainty. 37 This paper considers dose uncertainties in the TRDS-2016MC. Individual doses from 38 external and internal radiation sources were reconstructed for 48,036 people based on 39 environmental contamination patterns, residential histories, individual 90 Sr body-burden 40 measurements and dietary intakes. Dietary intake of 90 Sr resulted in doses accumulated in active 41 marrow (or simply, marrow) that were an order of magnitude greater than those in soft tissues. 42 About 84% of the marrow dose and 50% of the stomach dose was associated with internal 43 exposures. The lognormal distribution is well-fitted to the individual dose realizations, which, 44 therefore, could be expressed and easily operated in terms of geometric mean (GM) and geometric 45 standard deviation (GSD). Cohort average GM for marrow and stomach cumulative doses are 0.21 46 and 0.03 Gy, respectively. Cohort average dose uncertainties in terms of GSD are as follows: for 47 consistent with the data, which can be important in risk management. Confidence intervals are 73 also important when comparing results of studies from different populations. To date, only a few 74 studies of radiation effects have considered the quantitative impact of dose uncertainty, 75 particularly shared uncertainties, on risk estimates [3][4][5]. 76 Modern dosimetric systems should provide both central estimates of individual doses and 77 information on the uncertainty in these estimates. In particular, uncertainty information is needed 78 for the epidemiological studies of the Urals populations exposed to radiation from radioactive 79 environmental contamination that arose from the mid-20 th century discharges of radioactive 80 material from the Mayak Production Association (MPA). Population exposures were a 81 consequence of two major releases: the discharge of about 1x10 17 Bq of liquid waste into the 82 Techa River [6] between 1949 and 1956 and the atmospheric release of 7.4 * 10 16 Bq following 83 an explosion in a radioactive waste-storage facility in 1957 that formed the East Urals 84 Radioactive Trace (EURT) [7]. Members of the exposed populations received both external and 85 internal radiation exposures with bone-seeking long-lived 90 Sr making a significant contribution 86 to the internal dose. 87 Epidemiological studies in the Urals region provide a unique opportunity to quantify the 88 long-term effects of chronic, low-dose-rate exposure in a large, unselected population based on 89 follow-up of the Techa River Cohort (TRC) and the EURT Cohort (EURTC). Earlier risk 90 analyses have considered radiation effects in these two cohorts separately. However, since both 91 cohorts consist of rural residents of the same region with similar socio-economic status, similar 92 levels of medical care, and similar ethnic composition, it was recently decided to combine the 93 two cohorts. Risk analyses in the combined cohort, which includes 47,950 of the 48,036 94 individuals with TRDS16 dose realizations, will have more statistical power than those carried 95 out in the separate populations. About 5000 people in the combined cohort were exposed from 96 both the Techa River contamination and the releases from the 1957 accident. It should be noted 97 that, at this time, the combined cohort does not include people who were born after the initial 98 releases, i.e. 1950 for Techa River residents and September 29, 1957 for those exposed as a 99 consequence of the 1957 accident. 100 Epidemiological studies are based on a dosimetry system [8] that provides both a central 101 estimate as well as uncertainty of individual doses. Radiation doses for Urals residents have been 102 calculated with a set of computer codes known as the Techa River Dosimetry System (TRDS). modeling, it should be noted that the sources and the dynamics of dose formation for organs 114 other than the active marrow are similar, while the internal exposure to bone-seeking 90 Sr is a 115 significant, or even primary, source of marrow exposure. Therefore, the results presented here 116 focus on doses to the stomach, as a representative soft tissue dose, and active marrow. 117

TRDS-2016MC dosimetry system 118
In this section we outline the methods used to compute doses from internal and external 119 exposures by members of the combined TRC and EURTC and describe the nature of the 120 uncertainties in the dosimetric model parameters assumed for the Monte-Carlo dose 121 computations. 122 The TRDS performs dose calculations for 23 organs of 48,036 individuals over as much as 123 67 years by summing 4 dose components, viz: the Techa River internal exposure; the Techa 124 River external exposure; the EURT internal exposure, and the EURT external exposure. 125 For simplicity in this description, we assume that individuals stay in one location for whole 126 calendar years. However, the actual dose computations allow for people to live in multiple 127 locations for a given year. More detailed descriptions of the dosimetric models are given in [8, 128 10]. 129 The Techa River doses (1) 142 that depends on the following functions: 143  90 is the 90 Sr intake in year for a defined reference settlement; 144 is a ratio of the 90 Sr intake at location L i ( ) to that in the reference settlement; 145  α 90 ( i (y)) is the ratio of the 90 Sr intake in children to that in adults; 146  is an individualized 90 Sr intake scaling factor that depends on the availability of 147 individual or household 90 Sr measurements; 148 is a time-and location-dependent ratio used to convert 90 Sr intake to intake 149 of radioisotope . 150 The average-intake functions for the reference villages, I * y,r,L, (Eqn. 1), were the basis of the 151 Techa River internal dose reconstruction [11]. The uncertainty of these functions was a 152 significant contributor to the uncertainty of the Techa River internal doses [10]. These reference 153 functions were developed for two villages -Metlino and Muslyumovo (7 km and 78 km from 154 the site of releases, respectively). In Metlino, the use of the Techa River as a source of water 155 supply was prohibited in mid- August 1951. In 1953and 1954 were constructed in all other 156 Techa riverside villages to minimize the consumption of river water. Thus, Metlino residents 157 were supplied with non-contaminated water since August 1951, and in 1956 they were evacuated 158 to non-contaminated areas, primarily ONIS (New Metlino). As a result, the period of 90 Sr intake 159 was relatively short in Metlino. The temporal pattern of 90 Sr intake in Muslyumovo, which was 160 never evacuated, is typical for most other Techa River villages prior to their evacuation date (if 161 any). The time-dependent 90 Sr intake function for Muslyumovo was reconstructed using a 162 combination of 90 Sr measurements in teeth, measured 90 Sr concentrations in water and milk, and 163 estimates of water and milk consumption rates for adults and children. For Metlino, data on the 164 total-beta activity in excreta were also used [11]. The estimates of settlement-average-to-165 reference-village intake ratios ( L i (y) 90 , Eqn. 1) and corresponding village-specific shared 166 uncertainties were based on the normalized 90 Sr-body burdens in residents who lived 167 continuously in the settlement of interest from 1950 until at least 1953, a period during which 168 95% of total 90 Sr intake occurred. The main factor that determines L i (y) 90 variability within a 169 specific village is the residents' primary water supply. The ratios of 90 Sr intakes for different age 170 groups to that for adults living in the reference settlement (α 90 , Eqn. 1) were estimated using 171 age-dependence of water-and milk-consumption rates and measurements of the ratio of 90 Sr-172 concentration in milk to that in river water. Note that for most radionuclides, children-to-adult 173 intake ratios are the same as for 90 Sr since the main source of the intakes was the river water. 174 One exception is 137 Cs, which was additionally ingested with milk [11]. The model parameters 175 and their uncertainty structure are described in Table 1. 176 These estimates of the individual radioisotope-specific annual activity intake are converted 177 to the isotope-specific internal doses in various organs. The estimated dose to organ o associated 178 with the first year of chronic intake, 0 , from a given radioisotope is denoted as ( , ( 0 )), 179 where y is the year of interest. This dose can be computed with a single intake approach using 180 the following expression (Eqn. 2): 181 ( 0 )) is a dose coefficient to convert the radionuclide activity ingested in 183 year y0 to organ dose accumulated by the year of interest, y, (Bq to Gy). The dose factors are 184 developed using biokinetic and dosimetric models. Accounting for chronic intake, the total 185 (3) 187 The total Techa internal dose to an organ in year y summed over all radionuclides can be written 188 ( ( )) -residence to riverbank dose ratio at location L(y); 206 -ratio of the dose rate inside the house to that outside the house. 207 The total external dose to a specific organ arising from Techa River exposures is given by Eqn. 208 (6). 209

EURT doses 211
The doses received by EURT residents arose from exposure to 144 Ce, 95 Zr, 95 Nb, 90 Sr and 212 106 Ru. Internal exposure was from the ingestion of contaminated milk and foodstuff; external 213 exposure was due to surface deposition of these radionuclides, considered to be associated with 214 90 Sr deposition. Surface contamination of soil with 90 Sr was estimated based on the results of 215 measurements of the dose rate of gamma radiation and the specific activity of radionuclides in 216 environmental objects, which were performed immediately after the incident. Information on 217 food contamination was also available and has been used for internal dose reconstruction. 218

EURT internal dose 219
As with the Techa internal doses, the TRDS system provides separate internal organ dose 220 estimates for each radioisotope that are then summed to provide time-dependent estimates of the 221 annual organ doses. The expression for the annual radioisotope intake is (Eqn. 7) 222 where: 224 90 ( ( )) -surface 90 Sr contamination of soil in the location ( ) in year y; 225 Ε ( , ( ) ) -conversion factor for 90 / 2 to annual intake (Bq) for radioisotope r. 226 The estimated total internal organ dose in year y arising from chronic intakes since y0 is 227 computed as (Eqn. 8): 228 where, as with the Techa internal doses, ( − 0 , ( 0 )) is a dose factor that accounts for 230 biokinetic and dosimetric effects to convert ingested radionuclide activity to organ dose. This 231 dose factor is a function of age at intake and the time since the activity of interest was received. 232

EURT external dose 233
The EURT external dose depends on individual residence history and behavior patterns (time 234 spent inside the house). This annual dose was calculated as (Eqn. 9) 235 where 237 90 (L( )) -normalized absorbed EURT fallout dose rate in air at location L(y); 238 3 -proportion of time spent inside house (the same as for the Techa River); 239 -ratio of the dose rate inside the house to that outside the house (the same as for the Techa 240 River). 241

Monte Carlo dose realizations with shared and unshared uncertainties 242
The parameters of Equations (1-9) are defined and elaborated in the frame of long-term study 243 and summarized in [8,13]. Time and settlement-specific parameters are organized in the 244 databases. Other parameters were characterized by distribution functions. The TRDS-2016MC 245 databases include information on time-dependent radionuclide intakes and absorbed doses in air 246 for 41 settlements located along the Techa River downstream from the site of radioactive 247 releases to the mouth of the river, and 83 settlements located in the EURT area with initial 248 deposition of 90 Sr from 3.7 to 17800 kBq m -2 . The data for eight radionuclides ( 89 Sr, 90 Sr, 95 Zr, 249 95 Nb, 103 Ru, 106 Ru, 137 Cs, and 144 Ce) are considered. Each radionuclide has a separate table of 250 age-dependent dose coefficients providing absorbed dose in organ o per unit intake. Table 1  251 presents the general description of the parameters and their uncertainty distribution. The 252 characteristics of the distributions are presented in terms of multipliers on the arithmetic mean 253 (equal to that in the deterministic version of TRDS). Details of data sources for parameter 254 uncertainty distributions are presented in Supporting Information (S1). These distributions 255 reflected our understanding of the nature of the uncertainties as the system was developed. 256 As seen in Table 1, the behavioral parameters ( 1 , 2 , and T3) and the residence type and 257 location parameters ( ( ( )) and ) were considered to have no shared uncertainties. 258 The location-dependent annual dose rate in air on the banks for the Techa ( ( , ( )) ) and in 259 the EURT ( 90 (L( ))) were assumed to have shared uncertainties but no unshared 260 uncertainties. The remaining model parameters were assumed to have both shared and unshared 261 errors. The uncertainty in the intake parameters has a major effect on both the shared and 262 In the first step of the 2DMC process, a set of multiplicative shared uncertainty factors was 268 sampled from the parameter-specific shared uncertainty distributions for each realization and used 269 to compute a set of model parameters, which were stored in a database with one record per 270 realization. This sampling was done using a Latin hypercube sampling [14,15] procedure that 271 requires at least one realization per parameter in the dosimetry system. As seen in Table 1   about one third of the corresponding TR doses. The dose difference between organs is due to the 317 weak photon-energy dependence of the absorbed-dose-in-air to absorbed-dose-in-organ o, Ao 318 (Eqn. 1). The external exposure in the Urals region was mainly due to environmentally 319 distributed 137 Cs/ 137m Ba, 95 Zr, 95 Nb, 144 Ce/ 144 Pr/ 144m Pr and 106 Ru/ 106 Rh which are gamma-emitters 320 with photon energies within the range of 81 -1050 keV. However, there is a large plateau in the 321 energy dependence of A0 between about 80 and 1300 keV. Therefore, the mean value of A0 these 322 gamma-emitters was fixed to be equal to those typical of 137 Cs/ 137m Ba [16]. In other words, the 323 width of individual dose distribution is not organ specific. Therefore, the mean GSD and CV are 324 equal for marrow and stomach. On average, the uncertainties of cumulative EURT external doses 325 are 15% lower than those for the Techa River doses. This is mainly due to the shorter period of 326 exposure at EURT, where the short-lived radionuclides were the main contributors. Distributions 327 of individual external dose uncertainties in terms of GSD are shown in Fig. 1a and b for those 328 who were exposed from the Techa River and in the EURT, respectively. As one would expect 329 the CV of the population means (in the CV column of the mean dose rows in the

337
The Techa River GSD distribution has five modes indicated by the numbered arrows in Fig. 1a. 338 The first mode corresponds to GSD = 1.91 (CV~75%), the second -GSD=2.4 (CV~110%), the 339 third -GSD=2.65 (CV~120%), the fourth -GSD=2.9 (CV~130%) and the fifth -GSD=3.3 340 (CV~140%). The cumulative dose uncertainties largely depend on residence in the year of initial 341 exposure, the duration of residence in contaminated areas, and movements between settlements 342 in contaminated area. 343 For permanent residents (at least in the period from 1950 to 1956), the GSD modes are largely 344 due to uncertainties of the outdoor-to-riverbank dose rate ratio parameter -( ( )). TRDS-345 2016MC applies a subdivision of 9 Upper Techa settlements into 47 territories with homogenous 346 conditions of external exposure (clusters) based on information available. The mean of the 347 cluster-specific ( ( )) and the range of possible values were considered as unshared 348 parameters when simulating the variability of the rates within a cluster (Supporting information 349 S1). For the Middle and Lower Techa villages the settlement-average ( ( )) value is used. 350 The lowest values of ( ( )) uncertainty were typically for individuals with known 351 household location within a village. The houses in three small settlements from the lower reaches 352 (Vetrodujka, Zamanikha and Russkaya Techa) were parallel to the river so that the range of 353 possible values of ( ( )) was small and, accordingly, the uncertainties of this parameter 354 were comparable to that for the village-specific clusters in the Upper Techa. Generally, the 355 uncertainty of ( ( )) values in the village-specific clusters was proportional to the mean 356 value of the parameter. For example, people in GSD mode 1 were typically residents of Metlino 357 (7 km from the release site) for whom Rout/Riv,L >0.03; the second mode corresponds to 0.006 358 <Rout/Riv,L <0.03; the third one to 0.006 > Rout/Riv,L. 359 Modes 4 and 5 include people with doses calculated based on village-average ( ( )). The 360 difference between the modes of these two groups depends primarily on the residence history, 361 age at time of exposure (correlated to time spent at shoreline), and distance from the release site. 362 The maximum uncertainties are typical of the smallest doses. For example, cumulative doses in 363 the Lower Techa region (>200 km from site of releases) are almost always less than 4 mGy; 364 while the GSDs are quite large (>3). 365 The distribution of individual GSDs of cumulative EURT organ doses has two 366 pronounced modes (Fig. 1b), with GSDs of 2.06 (CV~78%) and 2.25 (CV~105%), respectively. 367 The two groups largely reflect age at exposure during the year, which is correlated with time 368 spent indoors. The first group consists of those whose age were less than 7 or older than 60 at the 369 time of the accident in 1957 (the outdoor time fraction <30%). The second mode reflects people 370 of ages between 7 and 59. The variability within the modes reflects uncertainties induced by 371 individual residence histories. 372

387
Person 2 is an individual born in 1943, initially exposed in the EURT (Russkaya Karabolka, 388 2427 kBq m -2 ) until evacuation to Russkaya Techa, on the Techa River 137 km from the site of 389 releases, in 1958. The mean cumulative EURT stomach dose was 0.04 Gy (CV=82%); 390 GSD=2.07 (the first mode in Fig.1b). Between 1958 and 1970 this person received an additional 391 0.002 Gy with a GSD=2.58 (the third mode in Fig. 1a). 392 For Person 1, the total mean cumulative dose was dominated by the mean cumulative TR dose 393 which exceeded the mean cumulative EURT dose by two orders of magnitude and essentially 394 determined the total probability density function (Fig. 2b). In the second case, the mean EURT 395 dose was, on average, an order of magnitude greater than the TR dose with a slight realization 396 overlap (< 5%) with those for the Techa River. The total cumulative dose distribution of total 397 doses was largely determined by the EURT dose. The lognormal-like asymmetry of these dose 398 distributions is typical of those for most exposures. Smoothing of histograms of cumulative dose 399 densities were computed using non-parametric kernel density estimation [17]. The distributions 400 of the individual total external stomach dose realizations for each of these people were well-401 described as lognormal. 402

Internal doses 403
In contrast to external exposure, the main contributors of internal dose in bone marrow and 404 stomach or other soft tissues differ markedly. Soft tissues were primarily exposed due to 405 circulating radionuclides during the intake period. The marrow was chronically exposed to the 406 activity of long-lived bone-seeking 90 Sr throughout their lives in addition to the circulating 407 radionuclides. For 90 Sr, both the biokinetic and dosimetric models are quite different for marrow 408 and soft tissue doses. Therefore, uncertainties of marrow and soft tissue dose coefficients 409 ( ( − 0 , ( 0 )) . 2) comprised of dosimetric and biokinetic models also differed. 410 Table 3 summarizes the distribution of internal doses (from both the Techa River and EURT) 411 and corresponding organ-specific uncertainties for stomach and marrow. As seen in Table 3, the 412 mean total cumulative internal stomach doses from the Techa River were as large as 541 mGy 413 with a mean (median) of 31 (5.8) mGy. Because of the chronic bone surface exposures, Techa 414 River internal marrow doses were about 10 times the internal stomach doses with a mean 415 (median) of 294 (37) mGy and a maximum of slightly more than 6.7 Gy. On average, EURT 416 internal exposures are less than 10% of the corresponding Techa River exposures (Table 3). 417 418 For Techa River residents with 90 Sr body burden measurements, it was possible to estimate a 422 time-integrated individual-to-model-ratio ( ) value that reflects the ratio of the individual 423 body burden to the village-average age-and gender-specific body burden predicted by the 424 strontium biokinetic model [18]. When IMRs were available within a household, the average of 425 the household-member-specific IMRs were used to define a Household-specific-ratio ( ) that 426 was then used to adjust the village-average intake for other cohort members who lived in the 427 same household. This approach made it possible to avoid explicit simulation of the various 428 components of drinking water source, diet, uptake, or metabolism that affect i ,r (L i (y), i (y)) 429 and greatly simplifies the uncertainty description (which becomes mainly unshared Ru) to internal exposure is an additional source of internal dose uncertainty. This 436 contribution was described using time-dependent, radionuclide-specific ratios of nuclide-to-90 Sr 437 intake ( L i (y) : 90 ). Radionuclide intake for the Techa River settlements was primarily from 438 drinking water. Radionuclide-specific ratios at different locations along the stream were 439 estimated based on models for radionuclide transport in the river [12]. The uncertainties of 440 portion is shared and a portion unshared between members of the cohort. For non-strontium 478 radionuclides, intakes were estimated based on data on total beta-activity in foodstuff adjusted 479 for radionuclide composition. In contrast to dose reconstruction for the Techa River, EURT 480 doses were not individualized, and the primary source of individual-to-individual variation in 481 cumulative dose uncertainties was related to residence history. 482 As for the Techa doses, bone seeking 90 Sr had a marked influence on the marrow dose. The first 483 peak in the EURT marrow GSD density (Fig. 3c) corresponds to the data for people with short-484 term intakes, mainly residents of three settlements (Berdyanish, Satlykovo, and Galikaeva) 485 located in the most contaminated EURT area (17,760 kBq m -2 of 90 Sr deposition), which were 486 evacuated within 7-14 days after the accident. The average 90 Sr exposure was almost 500 kBq of 487 90 Sr per stay. The first peak (GSD=2.8; CV~140%) is mainly defined by the uncertainty of , . 488 The second peak (GSD=3.74; CV~200%) is the modal value for all other EURT residents. 489 Non-strontium isotopes were the main source of soft tissue exposure in the initial period after the 490 incident [19]. For example, for settlements evacuated during the first two weeks after the 491 explosion, the isotope-to-strontium concentration ratios were considered as follows: 144 Ce-121; 492 106 Ru-7; 95 Zr-34; 95 Nb-57; 137 Cs-0.64. Information on non-strontium-radionuclide 493 contamination of food is limited, therefore, intake estimates for the early exposure periods were 494 highly uncertain. As a result, the 3 rd peak of stomach dose uncertainty distribution in Fig. 3d  495 (GSD=3.59, CV~240%) corresponds to doses calculated for residents evacuated within two 496 weeks of the explosion. The 1 st and 2 nd peaks in Fig. 3d (GSD=2.98, CV~190% and GSD=3.24, 497 CV~210%, respectively) are based on the much larger number of exposed people who were 498 evacuated at later dates or were never evacuated. Clustering of these data depended mainly on 499 the age at the initial intake, usually the time of the accident. Group 1 is dominated by individuals 500 whose were infants (0-2 years old) in 1957 and for whom individual variability in diets does not 501 play a big role in the structure of overall uncertainty. 502 The dose uncertainty for EURT exposure was much higher due to the high contribution of non-523 strontium isotopes (GSD~3.8). However, the cumulative doses from EURT exposures (<0.002 524 Gy) were 2 to 3 orders of magnitude lower than the Techa River doses (0.9 and 0.26 Gy for 525 marrow and stomach, respectively). 526 In contrast, person 4 was a female born in 1948 who resided along the Techa River in Novoe 527 Asanovo, 30 km from the site of releases from 1950 until she moved to ONIS in 1955. Following 528 the 1957 accident, surface contamination levels in ONIS were estimated to be 56 kBq m -2 of 90 Sr 529 surface contamination. The internal dose estimates for this person (1.05 Gy and 0.07 Gy for total 530 marrow and total stomach doses, respectively) are highly uncertain (CVs are 160% and 135%, 531 respectively) since they had no 90 Sr measurements and the exposures were based on settlement-532 average values. Geometric means are 0.56 Gy and 0.04 Gy, respectively. The GSDs were 533 calculated to be about 4 for total marrow dose and 3.3 for total stomach dose. The contribution to 534 the doses arising from residence in the EURT is on average 2 orders of magnitude lower than 535 that for the Techa River. However, in a small proportion of the realizations the EURT dose is 536 slightly greater than the TR dose 537 The plots in the bottom row for each person illustrate the cumulative dose realization densities at 538 the end of follow-up. The solid lines are smoothed kernel density estimates computed using the 539 KDE non-parametric approach. In each of these cases, the densities suggest a skewed lognormal-540 like distribution. 541 Total absorbed doses 542 Table 4 summarizes the population and individual uncertainties in individual total cumulative 543 marrow and stomach dose for all members of the combined cohort. This is the sum of the annual 544 internal and external doses arising from both Techa River and EURT exposures. 545 Table 4  Typically, among cohort members with both TR and EURT exposures, doses from EURT 549 exposure were lower than those from Techa River (as illustrated in Fig. 2 and Fig. 4 for persons 550 1, 3, and 4). As a result, for people with both TR and EURT exposures the uncertainty of total 551 dose was largely determined by the uncertainty of the Techa River dose components. 552 Radiation exposure in these environmentally exposed Urals' populations resulted in nonuniform 553 dose accumulation within the body. Bone-seeking 90 Sr results in marrow doses that are at least 554 an order of magnitude higher than soft tissue doses. For most cohort members, internal exposure 555 was the largest component of the total marrow dose, comprising more than half of the 556 cumulative marrow dose for 92% of cohort members. The cohort-average contribution of 557 internal dose to total marrow dose was 84%. Therefore, the total marrow dose GSD density (Fig.  558 5a) has a narrow peak at 2.2 and long tail up to 5 like that seen for the internal Techa River dose 559 component (Fig. 3a). External dose uncertainty also contributed to the marrow dose uncertainty. 560 This uncertainty is reflected in the mode around a GSD near 2.5reflecting the modal GSDs 561 around 2.4 and 2.7 seen in the Techa River external dose estimates (Fig. 1a). In general, people 562 for whom the GSD is less than 3 are cohort members with individualized external and/or internal 563 doses. The larger marrow GSDs were seen for people whose doses were based on group average 564 exposure estimates, which result in larger shared uncertainties. Averaging over all cohort members, 52% of the stomach dose was from internal exposure. In 569 particular, internal exposure accounts for less than half of the total stomach dose for roughly 570 50% of the survivors. Nevertheless, the pronounced multimodality seen for TR external dose 571 ( Fig. 1a) is less apparent when looking at total stomach dose (Fig. 5b). Uncertainty of total 572 stomach dose clusters in 2 peaks and a long tail. The first peak, around a GSD of 1.8, is typical 573 of the Techa River residents with individualized estimates for both the external and internal dose 574 components. The peak around a GSD of 2.3 corresponds to doses for people with limited 575 individualization, while the long tail reflects the uncertainty in people for whom there was no 576 individualization. 577 We examined the nature of the cumulative distributions of the realizations for individual cohort 578 members by determining which of several candidate distributions best described the empirical 579 distribution of total dose for that person. The goodness of fit was assessed using one-sample 580 Kolmogorov-Smirnov (K-S) tests [20] for each member of the combined (EURT + the Techa 581 River) cohort. The best fitting distribution was taken to be the candidate distribution with the 582 largest P-value greater than 0.05. If the P-values for each of candidate distributions was less than 583 0.05, we indicate that none of the distributions fit well. Table 5 shows the proportion of the best 584 fitting cumulative distributions for individual dose realizations by exposure type and source 585 components for the total dose. 586 The distributions of dose estimates over dose realization for individual cohort members were 587 highly skewed to the right, which is to be expected given the nature and complexity of the 588 uncertainty factor distributions. For both Techa River internal and external total cumulative 589 doses, the dose realization distributions were well described by lognormal distributions for more 590 than two-thirds of the cohort members. For doses attributed to EURT internal exposures, the best 591 fitting distributions were lognormal for more than 95% of the cohort members. For external 592 exposures arising from EURT exposures only about 40% of the distributions could be described 593 as lognormal and for 15% of the people scaled beta distributions provided the best fit. Except for 594 doses arising from EURT internal exposure, none of the distributions considered appeared to be 595 appropriate for 25% or more of the cohort members. 596

604
Examples of individuals for which the best fitting dose distribution was lognormal are shown in 605 the Fig. 2 (b, d) for total external dose and Fig. 4 (c, d, h) for total internal dose. The Techa 606 internal dose for Case 4 (Fig. 4g) is an example in which none of the candidate distributions 607 considered adequately described the empirical distribution. Typically, the K-S P-values for the 608 hypothesis of lognormality were between 0.3 and 0.9. For both marrow and stomach total doses, 609 the individual dose realization distributions were best described as lognormal for about 70% of 610 the cohort members. For cases in which a best-fitting distribution was chosen, the hypothesis of 611 lognormality could rarely be rejected at the P < 0.05 level. 612

613
The Techa River Dosimetry System (TRDS) has been developed over several decades to provide 614 dose estimates for people exposed from Mayak's releases of radioactive waste into the Techa 615 River in the early 1950s and from radioactive fallout in the EURT following the 1957 explosion 616 of a Mayak waste storage tank. Earlier versions of the TRDS provided deterministic estimates of 617 individual annual doses arising from both internal and external exposures with little useful 618 information on the uncertainty of these estimates. Uncertainty in dose estimates is a potential 619 source of systematic error (bias) and increased uncertainty in the assessment of radiation risks. 620 As described in [6,8,16,18,19], we have refined and improved the models and methods used to 621 estimate organ doses resulting from Techa River and EURT exposures. As part of this effort, we 622 have endeavored to characterize the uncertainty in the individual dose estimates. This was done 623 by determining the major sources of shared and unshared uncertainties in the dose estimates, 624 specifying distributions for these uncertainties, and using these distributions to develop multiple 625 realizations of individual annual organ doses for 48,036 people in the combined Techa River and 626 EURT cohorts. These distributions and the resulting 2-dimensional Monte-Carlo dosimetry 627 system [9] have been described in this paper. 628 While 90 Sr measurements that help reduce uncertainty in internal dose estimates are available for 629 many cohort members with Techa River exposures, for most of the factors leading to 630 uncertainties in individual internal and external dose estimates identified in Table 1 the nature of  631 the uncertainty distributions was based on expert judgment. As part of our efforts to validate 632 both the external doses and their uncertainties, we compared the individual TRDS-2016MC 633 mean total cumulative doses to individual dose estimates based on tooth enamel Electron 634 Paramagnetic Resonance (EPR) and Fluorescent In-Situ Hybridization (FISH) on lymphocytes 635 [21,22]. There was good agreement between these measurement-based dose estimates and mean 636 TRDS16-MC estimates. The EPR results could also be used to assess the uncertainty of external 637 radiation doses [23]. For the 220 people with EPR-based dose estimates, the 90% CI for the 638 EPR-based estimate was compared to the 90% CI TRDS-2016MC external dose estimates. 639 Looking at the comparison of cumulative probability distributions (cdf) of individual total 640 marrow and stomach doses (Fig. 6a,b), one can see that while the range of the individual GSDs 641 is relatively large for both marrow and stomach dose, the range is somewhat smaller for stomach 642 than for marrow dose. The main contributor to marrow dose uncertainty, especially for cohort 643 members with no individual 90 Sr body burden measurements, is the shared uncertainty (within 644 villages) in the intake function. On the other hand, while internal exposures contribute to the 645 uncertainty of the stomach dose (and other soft tissue dose) estimates (which use the same intake 646 functions as marrow doses), these doses also depend, to a large extent, on uncertainties in the 647 external exposures. Perhaps the marked contribution of unshared uncertainty in the behavior 648 parameters related to time spent in various locations as a function of age and location 649 ( 1 ( ( )), 2 ( ( )) and 3 ( ( ))) masks some of the shared uncertainties in the system. This could 650 explain why the variability in the individual stomach dose GSDs are smaller than those for 651 individual marrow doses. 652 It should also be noted that internal dose individualization with IMRs or HSRs is available for 653 about 40% of the members of the combined cohort. The marrow dose uncertainties for these 654 people are less than those for the 60% of the cohort whose marrow doses depend on the 655 relatively large uncertainties that arise from the potential bias (shared uncertainty) in the village 656 average IMRs. 657 Shared uncertainties result in systematic differences in the dose distributions for different dose 658 realizations. This is illustrated in Figure 6, which presents the cumulative distribution functions 659 of the ratio of the realization-specific total cumulative marrow (left plot) and stomach (right plot) 660 doses to the mean organ-specific population dose for four realizations. Because of shared 661 uncertainties within each realization, some realizations are systematically higher (150 and 450 662 for marrow dose in this figure) than others. As shared uncertainty increases, the between-663 realization spread of these cdfs will increase. The plots suggest that given the uncertainty 664 parameters used in TRDS-2016MC, shared uncertainty is more important for marrow than for 665 stomach doses. 666

670
As interest in assessing the effects of dose uncertainty on risk estimate uncertainty has increased, 671 Monte-Carlo dosimetry systems have been developed for a number of studies. [21] children, exposed to 131 I as a result of the Chornobyl accident; the combined TRC/EURTC 675 cohort; and members of the TRC exposed to 131 I due to airborne releases from Mayak [22]. 676  cohort. The doses due to 131 I were combined with the contribution of environmental 694 contamination and dietary intakes of other radionuclides. It should be noted, the non-Iodine 695 doses to the thyroid were comparable to those for stomach described above. The mean individual 696 iodine doses were as high as 7 Gy for residents who were born in the villages near the Mayak 697 plant in 1948. 698 The second [3] and third [21] studies listed in Table 6 involve residents of the most contaminated 699 territories of Ukraine and Belorussia with radioactive fallout from Chornobyl accident, who were 700 born before the fallout and were less than 18 years old at the time of the accident. Internal 701 thyroid doses were reconstructed based on the direct measurements of thyroid burden in April-702 June 1986 and personal information on residence and diet histories. These two cohorts are of 703 similar size and have similar dose and uncertainty sources. Individual measurements of 131 I in 704 thyroid reduce the impact of shared uncertainties. Therefore, one can expect the impact of dose 705 uncertainties on risk analysis for these cohorts to be negligible. In contrast, the effect of shared 706 uncertainties is expected to be larger for the other studies listed in Table 5 vector with the specified disease outcome, and using a Markov Chain Monte-Carlo (MCMC) 724 uncertainties affect risk estimate uncertainty. In developing the TRDS-2016MC system, we came 786 to realize how challenging it can be to make decisions about the uncertainty factors and how best 787 to characterize their distributions. In this report we have focused on our final decisions. We 788 cannot claim that the factors that we considered or that the distributions used are optimal or even 789 that we included all important sources of uncertainty. However, we hope that they provide a 790 reasonable assessment of the impact of dose uncertainty on risk estimate uncertainty. Now that 791 we have some tools for and experience in computing 2DMC dose realizations and in managing 792 the large amounts of data produced by these systems, it will be easier to investigate the impact of 793 different choices in the design of the system. 794 Furthermore, we think it would be useful and feasible for researchers who have or are 795 developing 2DMC systems to have some joint discussions in the hope of developing and 796 publishing basic guidelines for the development of these systems. 797